A181320 Triangle T(n,m) read by rows: the number of series-parallel networks with n+2 vertices and m+n+1 edges.

1, 1, 1, 2, 7, 5, 6, 48, 91, 49, 24, 360, 1304, 1697, 729, 120, 3000, 17910, 41440, 41051, 14641, 720, 27720, 249900, 899730, 1524282, 1218745, 371293

Offset: 0

Author

R. J. Mathar, Jan 26 2011

Keywords

• tabl
• nonn

Comments

Obtained by evaluating the half-exponential generating function D(x,y) in Lemma 3.1 of Drmota et al.

D(x,y) = sum_{n,m} d_(n,m)*x^n*y^m/n! with log( (1+D)/(1+y)) = x*D^2/(1+x*D).

The diagonal appears to be A052750.

Examples

			The table d_(n,m) [which is T(n,m) with leading zeros maintained] for the number of SP networks with n+2 vertices and m nodes (internal nodes labeled from 1 to n) starts in row n=0 with columns m>=0 as:
n\m| 0  1  2  3  4
----------------------
0  | 0  1
1  | 0  0  1  1
2  | 0  0  0  2  7  5
3  | 0  0  0  0  6 48  91  49
		

Links

• Michael Drmota, Omer Gimenez, Marc Noy, Vertices of given degree in series-parallel graphs, Rand. Struct. Algo. 36 (3) (2010) 273-314